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Zbl 1158.93413
Lu, Jianquan; Ho, Daniel W.C.; Wu, Ligang
Exponential stabilization of switched stochastic dynamical networks. (English)
[J] Nonlinearity 22, No. 4, 889-911 (2009). ISSN 0951-7715; ISSN 1361-6544/e

Summary: A Switched Stochastic Dynamical Network (SSDN) model will firstly be formulated in this paper, which considers two mutually independent switching signals including individual node switching and network topology switching. In the proposed SSDN model, the stochastic perturbation is described by multi-dimensional Brownian motion, and the switching signals are arbitrary under the constraint of the average dwell time. A multiple Lyapunov function is utilized to cope with the switching problem. A single controller is then designed for the exponential mean square stabilization for SSDNs. The coupling matrix of the SSDN can be assumed to be irreducible symmetric or irreducible asymmetric. The obtained criteria are given in terms of linear matrix inequalities, which can be solved efficiently by standard software packages. Numerical examples, including small-world and scale-free networks, are exploited to illustrate the effectiveness of the theoretical results. It can be observed from the examples that our results are also applicable to large-scale dynamical networks.

MSC 2000:: *93E15 Stochastic stability
94C10 Switching theory
90B15 Flows in networks with stochastic elements
93B51 Design techniques in systems theory

Keywords: switched stochastic dynamical network; stochastic perturbation; multiple Lyapunov function

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